Is it possible for an object to have zero velocity while still experiencing acceleration?

Yes, an object thrown vertically upward reaches a point of zero velocity at its highest point, yet it still experiences an acceleration equal to the acceleration due to gravity.

Is it possible for an object to have a velocity directed eastward while undergoing an acceleration directed westward?

Yes, a pendulum swinging in an east-west direction will have an eastward velocity and a westward acceleration during half of its oscillation cycle.

Can a body experience acceleration without changing its speed? If so, please provide an example.

Yes, an object in uniform circular motion is indeed accelerating, while its speed stays constant—it does not increase or decrease.

Are the direction of acceleration and the direction of velocity always the same?

Not necessarily. When velocity increases, acceleration acts in the same direction as the velocity, while if velocity decreases, acceleration acts in the opposite direction.

Which of the two—velocity or acceleration—indicates the direction of an object's motion? Please justify your answer with an example.

It is the velocity, not the acceleration, that indicates the direction of an object's motion. For instance, when a body is projected upward, both its direction of motion and velocity are upward, while the acceleration acts downward.

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JEE Physics

Acceleration

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Acceleration

Acceleration is a key concept in physics that alludes to the rate at which an object's velocity changes over time. As a vector quantity, it possesses both magnitude and direction. Acceleration takes place when a body speeds up, slows down, or alters its direction. We experience acceleration in many everyday scenarios, such as a car accelerating from a stoplight, a roller coaster picking up speed on a descent, or a planet orbiting the sun. Grasping the concept of acceleration is essential not only for physics but also for applications in engineering, sports science, and medicine.

1.0Acceleration

Rate of change of velocity is called acceleration.
It is a vector quantity.
Its direction is the same as that of change in velocity (not in the direction of the velocity).
Dimension Formula: [M⁰L¹T^–2]
Unit : (S.I.) m/s² (C.G.S.) cm/s²
There are 3 ways to change a velocity (vector)
Only magnitude change
Only direction change
Both direction or magnitude change

2.0Examples Of Acceleration

Gravity: When an object falls, like an apple dropping from a tree, it accelerates downward toward the ground because of the force of gravity.
Driving a Car: When you press the gas pedal to accelerate from a stop, the car moves forward more quickly. In contrast, applying the brakes causes the car to decelerate, effectively accelerating in the opposite direction.

3.0Types of Acceleration

Uniform Acceleration: A body is considered to have uniform acceleration if both the magnitude and direction of its acceleration remain constant throughout the motion of the particle.
Non-Uniform Acceleration: A body is described as having non-uniform acceleration if either the magnitude, the direction, or both change during its motion.
Average Acceleration: It is the ratio of the total change in velocity to the total time taken by the particle.

$a_{avg} = \frac{Change in Velocity}{Time Interval} = \frac{Δ v}{Δ t} = \frac{v _{f} - v _{i}}{Δ t}$

Direction of average acceleration is along the change in velocity.

Instantaneous Acceleration: Acceleration of an object at a specific moment in time.

$a_{inst} = lim_{Δ t \to 0} (\frac{Δ v}{Δ t}) \Rightarrow a_{inst} = \frac{dv}{dt}$ , where $v$ is function of time

First derivative of velocity is called Instantaneous Acceleration

$a = \frac{d v}{d t} = \frac{d ^{2} r}{d t ^{2}} (v = \frac{d r}{d t})$

Second derivative of position vector is called Instantaneous acceleration

$a = \frac{d v}{d t} \times \frac{d x}{d x} \Rightarrow v \frac{d v}{d x}$ , where v is the function of position x

Example: The relationship between time t and distance x is given by the equation $t = a x^{2} + b x$ , where a and b are constants. How can we express the instantaneous acceleration in terms of the instantaneous velocity?

Solution:

$t = a x^{2} + b x$

$\frac{d t}{d x} = 2 a x + b$

velocity,

$v = \frac{d x}{d t} = (2 a x + b)^{- 1}$

Acceleration,

$a = \frac{d v}{d t} = \frac{d v}{d x} \cdot \frac{d x}{d t} = v \frac{d v}{d x}$

$a = v \frac{d}{d x} (2 a x + b)^{- 1}$

$= v (- 1) (2 a x + b)^{- 2} \cdot 2 a = - 2 a (2 a x + b)^{- 3} = - 2 a v^{3}$

4.0Acceleration Due To Gravity

When a body falls freely towards the surface of earth, its velocity continuously increases. The acceleration yielded in a freely falling body under the gravitational pull of the Earth is called acceleration due to gravity.
It is a vector having direction towards the centre of Earth. It does not depend on the mass, size and shape of the body.
Value of g varies from place to place on the surface of Earth, it depends on altitude, depth, rotation of the Earth and Shape of the Earth.
Value of $g = 9.8 \frac{m}{s ^{2}}$ or $32 f t s^{- 2}$

Relation Between Acceleration due to Gravity(g) and Universal Gravitational Constant(G)

Relation between acceleration due to gravity (g) and gravitational constant G

$F = G \frac{M m}{R ^{2}}$ …………… (1)

$F = m g$ …………… (2)

$m g = G \frac{M m}{R ^{2}}$

$g = \frac{GM}{R ^{2}}$ , value of g is the unconstrained mass, size and shape of the body falling under gravity.

5.0Centripetal Acceleration

When an object is in uniform circular motion, its speed remains constant; however, its velocity continuously changes due to the shifting direction. As a result, the motion is considered accelerated.
A body in uniform circular motion experiences an acceleration directed radially inward toward the center of its circular path. This acceleration is known as centripetal (or center-seeking) acceleration.
$a = \frac{v ^{2}}{r} = ω^{2} r$
The direction of centripetal acceleration continuously changes and is always perpendicular to the velocity vector at every point along the path.

6.0Difference Between Acceleration and Velocity

Acceleration	Velocity
Rate of change of velocity over time	Rate of change of position over time
Change in speed or direction
Unit is meters per second squared (m/s²)	Unit is meters per second (m/s)
$a = \frac{d v}{d t}$	$v = \frac{d s}{d t}$

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Acceleration

Acceleration is a key concept in physics that alludes to the rate at which an object's velocity changes over time. As a vector quantity, it possesses both magnitude and direction. Acceleration takes place when a body speeds up, slows down, or alters its direction. We experience acceleration in many everyday scenarios, such as a car accelerating from a stoplight, a roller coaster picking up speed on a descent, or a planet orbiting the sun. Grasping the concept of acceleration is essential not only for physics but also for applications in engineering, sports science, and medicine.

1.0Acceleration

Rate of change of velocity is called acceleration.
It is a vector quantity.
Its direction is the same as that of change in velocity (not in the direction of the velocity).
Dimension Formula: [M⁰L¹T^–2]
Unit : (S.I.) m/s² (C.G.S.) cm/s²
There are 3 ways to change a velocity (vector)
Only magnitude change
Only direction change
Both direction or magnitude change

2.0Examples Of Acceleration

Gravity: When an object falls, like an apple dropping from a tree, it accelerates downward toward the ground because of the force of gravity.
Driving a Car: When you press the gas pedal to accelerate from a stop, the car moves forward more quickly. In contrast, applying the brakes causes the car to decelerate, effectively accelerating in the opposite direction.

3.0Types of Acceleration

Uniform Acceleration: A body is considered to have uniform acceleration if both the magnitude and direction of its acceleration remain constant throughout the motion of the particle.
Non-Uniform Acceleration: A body is described as having non-uniform acceleration if either the magnitude, the direction, or both change during its motion.
Average Acceleration: It is the ratio of the total change in velocity to the total time taken by the particle.

$a_{avg} = \frac{Change in Velocity}{Time Interval} = \frac{Δ v}{Δ t} = \frac{v _{f} - v _{i}}{Δ t}$

Direction of average acceleration is along the change in velocity.

Instantaneous Acceleration: Acceleration of an object at a specific moment in time.

$a_{inst} = lim_{Δ t \to 0} (\frac{Δ v}{Δ t}) \Rightarrow a_{inst} = \frac{dv}{dt}$ , where $v$ is function of time

First derivative of velocity is called Instantaneous Acceleration

$a = \frac{d v}{d t} = \frac{d ^{2} r}{d t ^{2}} (v = \frac{d r}{d t})$

Second derivative of position vector is called Instantaneous acceleration

$a = \frac{d v}{d t} \times \frac{d x}{d x} \Rightarrow v \frac{d v}{d x}$ , where v is the function of position x

Example: The relationship between time t and distance x is given by the equation $t = a x^{2} + b x$ , where a and b are constants. How can we express the instantaneous acceleration in terms of the instantaneous velocity?

Solution:

$t = a x^{2} + b x$

$\frac{d t}{d x} = 2 a x + b$

velocity,

$v = \frac{d x}{d t} = (2 a x + b)^{- 1}$

Acceleration,

$a = \frac{d v}{d t} = \frac{d v}{d x} \cdot \frac{d x}{d t} = v \frac{d v}{d x}$

$a = v \frac{d}{d x} (2 a x + b)^{- 1}$

$= v (- 1) (2 a x + b)^{- 2} \cdot 2 a = - 2 a (2 a x + b)^{- 3} = - 2 a v^{3}$

4.0Acceleration Due To Gravity

When a body falls freely towards the surface of earth, its velocity continuously increases. The acceleration yielded in a freely falling body under the gravitational pull of the Earth is called acceleration due to gravity.
It is a vector having direction towards the centre of Earth. It does not depend on the mass, size and shape of the body.
Value of g varies from place to place on the surface of Earth, it depends on altitude, depth, rotation of the Earth and Shape of the Earth.
Value of $g = 9.8 \frac{m}{s ^{2}}$ or $32 f t s^{- 2}$

Relation Between Acceleration due to Gravity(g) and Universal Gravitational Constant(G)

$F = G \frac{M m}{R ^{2}}$ …………… (1)

$F = m g$ …………… (2)

$m g = G \frac{M m}{R ^{2}}$

$g = \frac{GM}{R ^{2}}$ , value of g is the unconstrained mass, size and shape of the body falling under gravity.

5.0Centripetal Acceleration

When an object is in uniform circular motion, its speed remains constant; however, its velocity continuously changes due to the shifting direction. As a result, the motion is considered accelerated.
A body in uniform circular motion experiences an acceleration directed radially inward toward the center of its circular path. This acceleration is known as centripetal (or center-seeking) acceleration.
$a = \frac{v ^{2}}{r} = ω^{2} r$
The direction of centripetal acceleration continuously changes and is always perpendicular to the velocity vector at every point along the path.

6.0Difference Between Acceleration and Velocity

Acceleration	Velocity
Rate of change of velocity over time	Rate of change of position over time
Change in speed or direction
Unit is meters per second squared (m/s²)	Unit is meters per second (m/s)
$a = \frac{d v}{d t}$	$v = \frac{d s}{d t}$

Frequently Asked Questions

Is it possible for an object to have zero velocity while still experiencing acceleration?

Is it possible for an object to have a velocity directed eastward while undergoing an acceleration directed westward?

Can a body experience acceleration without changing its speed? If so, please provide an example.

Are the direction of acceleration and the direction of velocity always the same?

Which of the two—velocity or acceleration—indicates the direction of an object's motion? Please justify your answer with an example.

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Acceleration

1.0Acceleration

2.0Examples Of Acceleration

3.0Types of Acceleration

4.0Acceleration Due To Gravity

5.0Centripetal Acceleration

6.0Difference Between Acceleration and Velocity

Table of Contents

Frequently Asked Questions

Is it possible for an object to have zero velocity while still experiencing acceleration?

Is it possible for an object to have a velocity directed eastward while undergoing an acceleration directed westward?

Can a body experience acceleration without changing its speed? If so, please provide an example.

Are the direction of acceleration and the direction of velocity always the same?

Which of the two—velocity or acceleration—indicates the direction of an object's motion? Please justify your answer with an example.

Join ALLEN!

Acceleration

1.0Acceleration

2.0Examples Of Acceleration

3.0Types of Acceleration

4.0Acceleration Due To Gravity

5.0Centripetal Acceleration

6.0Difference Between Acceleration and Velocity

Table of Contents